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Who said: “I have no satisfaction in formulas unless I feel their arithmetical magnitude.”
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Home > Category Index for Science Quotations > Category Index P > Category: Proportion

Proportion Quotes (136 quotes)

À mesure que la science rabaisse ainsi notre orgueil, elle augmente notre puissance.
Science increases our power in proportion as it lowers our pride.
Original French quote from Introduction à l’étude de la médecine expérimentale (1865), 141. As translated in Fielding H. Garrison, 'Medical Proverbs, Aphorisms and Epigrams', Bulletin of New York Academy of Medicine (Oct 1928), 4, No. 10, 997. The translation above is literal. For a clearer interpretation, see another version on this web page: “But by a marvellous compensation, science, in humbling our pride, proportionately increases our power.”
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Branches or types are characterized by the plan of their structure,
Classes, by the manner in which that plan is executed, as far as ways and means are concerned,
Orders, by the degrees of complication of that structure,
Families, by their form, as far as determined by structure,
Genera, by the details of the execution in special parts, and
Species, by the relations of individuals to one another and to the world in which they live, as well as by the proportions of their parts, their ornamentation, etc.
Essay on Classification (1857). Contributions to the Natural History of the United States of America (1857), Vol. I, 170.
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Ce grand ouvrage, toujours plus merveilleux à mesure qu’il est plus connu, nous donne une si grande idée de son ouvrier, que nous en sentons notre esprit accablé d’admiration et de respect.
[The Universe] This great work, always more amazing in proportion as it is better known, raises in us so grand an idea of its Maker, that we find our mind overwhelmed with feelings of wonder and adoration.
Original French and translation in Craufurd Tait Ramage (ed.) Beautiful Thoughts from French and Italian Authors (1866), 119-120.
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Mais, par une merveilleuse compensation, à mesure que la science rabaisse ainsi notre orgueil, elle augmente notre puissance.
But by a marvellous compensation, science, in humbling our pride, proportionately increases our power.
Original French quote from Introduction à l’étude de la médecine expérimentale (1865), 141. As translated by H.C. Greene in An Introduction to the Study of Experimental Medicine (1927, 1949), 82. Most often seen quoted in a shorter, more literal translation as “Science increases our power in proportion as it lowers our pride” (detailed elsewhere on this web page).
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A cosmic mystery of immense proportions, once seemingly on the verge of solution, has deepened and left astronomers and astrophysicists more baffled than ever. The crux ... is that the vast majority of the mass of the universe seems to be missing.
[Reporting a Nature article discrediting explanation of invisible mass being due to neutrinos]
In 'If Theory is Right, Most of Universe is Still “Missing”', New York Times (11 Sep 1984).
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A large proportion of mankind, like pigeons and partridges, on reaching maturity, having passed through a period of playfulness or promiscuity, establish what they hope and expect will be a permanent and fertile mating relationship. This we call marriage.
Genetics And Man (1964), 298.
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A surprising proportion of mathematicians are accomplished musicians. Is it because music and mathematics share patterns that are beautiful?
In 'Introduction' contributed to Donald J. Albers and Gerald L. Alexanderson, More Mathematical People: Contemporary Conversations (1990), xi.
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An error is the more dangerous in proportion to the degree of truth which it contains.
Entry for 26 Dec 1852 in Amiel’s Journal: The Journal Intime of Henri-Frédéric Amiel, trans. Humphry Ward (1893), 34.
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And if you want the exact moment in time, it was conceived mentally on 8th March in this year one thousand six hundred and eighteen, but submitted to calculation in an unlucky way, and therefore rejected as false, and finally returning on the 15th of May and adopting a new line of attack, stormed the darkness of my mind. So strong was the support from the combination of my labour of seventeen years on the observations of Brahe and the present study, which conspired together, that at first I believed I was dreaming, and assuming my conclusion among my basic premises. But it is absolutely certain and exact that the proportion between the periodic times of any two planets is precisely the sesquialterate proportion of their mean distances.
Harmonice Mundi, The Harmony of the World (1619), book V, ch. 3. Trans. E. J. Aiton, A. M. Duncan and J. V. Field (1997), 411.
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And thus Nature will be very conformable to her self and very simple, performing all the great Motions of the heavenly Bodies by the Attraction of Gravity which intercedes those Bodies, and almost all the small ones of their Particles by some other attractive and repelling Powers which intercede the Particles. The Vis inertiae is a passive Principle by which Bodies persist in their Motion or Rest, receive Motion in proportion to the Force impressing it, and resist as much as they are resisted. By this Principle alone there never could have been any Motion in the World. Some other Principle was necessary for putting Bodies into Motion; and now they are in Motion, some other Principle is necessary for conserving the Motion.
From Opticks, (1704, 2nd ed. 1718), Book 3, Query 31, 372-3.
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André Weil suggested that there is a logarithmic law at work: first-rate people attract other first-rate people, but second-rate people tend to hire third-raters, and third-rate people hire fifth-raters. If a dean or a president is genuinely interested in building and maintaining a high-quality university (and some of them are), then he must not grant complete self-determination to a second-rate department; he must, instead, use his administrative powers to intervene and set things right. That’s one of the proper functions of deans and presidents, and pity the poor university in which a large proportion of both the faculty and the administration are second-raters; it is doomed to diverge to minus infinity.
In I Want to be a Mathematician: an Automathography (1985), 123.
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Anyone of common mental and physical health can practice scientific research. … Anyone can try by patient experiment what happens if this or that substance be mixed in this or that proportion with some other under this or that condition. Anyone can vary the experiment in any number of ways. He that hits in this fashion on something novel and of use will have fame. … The fame will be the product of luck and industry. It will not be the product of special talent.
In Essays of a Catholic Layman in England (1931).
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As an antiquary of a new order, I have been obliged to learn the art of deciphering and restoring these remains, of discovering and bringing together, in their primitive arrangement, the scattered and mutilated fragments of which they are composed, of reproducing in all their original proportions and characters, the animals to which these fragments formerly belonged, and then of comparing them with those animals which still live on the surface of the earth; an art which is almost unknown, and which presupposes, what had scarcely been obtained before, an acquaintance with those laws which regulate the coexistence of the forms by which the different parts of organized being are distinguished.
'Preliminary discourse', to Recherches sur les Ossemens Fossiles (1812), trans. R. Kerr Essay on the Theory of the Earth (1813), 1-2.
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As I strayed into the study of an eminent physicist, I observed hanging against the wall, framed like a choice engraving, several dingy, ribbon-like strips of, I knew not what... My curiosity was at once aroused. What were they? ... They might be shreds of mummy-wraps or bits of friable bark-cloth from the Pacific, ... [or] remnants from a grandmother’s wedding dress... They were none of these... He explained that they were carefully-prepared photographs of portions of the Solar Spectrum. I stood and mused, absorbed in the varying yet significant intensities of light and shade, bordered by mystic letters and symbolic numbers. As I mused, the pale legend began to glow with life. Every line became luminous with meaning. Every shadow was suffused with light shining from behind, suggesting some mighty achievement of knowledge; of knowledge growing more daring in proportion to the remoteness of the object known; of knowledge becoming more positive in its answers, as the questions which were asked seemed unanswerable. No Runic legend, no Babylonish arrowhead, no Egyptian hieroglyph, no Moabite stone, could present a history like this, or suggest thoughts of such weighty import or so stimulate and exalt the imagination.
The Sciences of Nature Versus the Science of Man: A Plea for the Science of Man (1871), 7-9.
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Bearing in mind that it is from the vitality of the atmospheric particles that all the mischief arises, it appears that all that is requisite is to dress the wound with some material capable of killing these septic germs, provided that any substance can be found reliable for this purpose, yet not too potent as a caustic. In the course of the year 1864 I was much struck with an account of the remarkable effects produced by carbolic acid upon the sewage of the town of Carlisle, the admixture of a very small proportion not only preventing all odour from the lands irrigated with the refuse material, but, as it was stated, destroying the entozoa which usually infest cattle fed upon such pastures.
'On a New Method of Treating Compound Fracture, Abscesses, etc: With Observations on the Conditions of Supperation', Part 1, The Lancet (1867), 327.
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Benford's Law of Controversy: Passion is inversely proportional to the amount of real information available.
In novel, Timescape (1992), no page numbering. The reference in the orginal text uses the past tense.
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Beyond these are other suns, giving light and life to systems, not a thousand, or two thousand merely, but multiplied without end, and ranged all around us, at immense distances from each other, attended by ten thousand times ten thousand worlds, all in rapid motion; yet calm, regular and harmonious—all space seems to be illuminated, and every particle of light a world. ... all this vast assemblages of suns and worlds may bear no greater proportion to what lies beyond the utmost boundaries of human vision, than a drop of water to the ocean.
In The Geography of the Heavens and Class-Book of Astronomy (1874), 148 That knowledge is not happiness.
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But many of our imaginations and investigations of nature are futile, especially when we see little living animals and see their legs and must judge the same to be ten thousand times thinner than a hair of my beard, and when I see animals living that are more than a hundred times smaller and am unable to observe any legs at all, I still conclude from their structure and the movements of their bodies that they do have legs... and therefore legs in proportion to their bodies, just as is the case with the larger animals upon which I can see legs... Taking this number to be about a hundred times smaller, we therefore find a million legs, all these together being as thick as a hair from my beard, and these legs, besides having the instruments for movement, must be provided with vessels to carry food.
Letter to N. Grew, 27 Sep 1678. In The Collected Letters of Antoni van Leeuwenhoek (1957), Vol. 2, 391.
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Come, see the north-wind’s masonry, Out of an unseen quarry evermore Furnished with tile, the fierce artificer Curves his white bastions with projected roof Round every windward stake, or tree, or door. Speeding, the myriad-handed, his wild work So fanciful, so savage, naught cares he For number or proportion.
…...
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De Morgan was explaining to an actuary what was the chance that a certain proportion of some group of people would at the end of a given time be alive; and quoted the actuarial formula, involving p [pi], which, in answer to a question, he explained stood for the ratio of the circumference of a circle to its diameter. His acquaintance, who had so far listened to the explanation with interest, interrupted him and exclaimed, “My dear friend, that must be a delusion, what can a circle have to do with the number of people alive at a given time?”
In Mathematical Recreations and Problems (1896), 180; See also De Morgan’s Budget of Paradoxes (1872), 172.
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ENGINEER, in the military art, an able expert man, who, by a perfect knowledge in mathematics, delineates upon paper, or marks upon the ground, all sorts of forts, and other works proper for offence and defence. He should understand the art of fortification, so as to be able, not only to discover the defects of a place, but to find a remedy proper for them; as also how to make an attack upon, as well as to defend, the place. Engineers are extremely necessary for these purposes: wherefore it is requisite that, besides being ingenious, they should be brave in proportion. When at a siege the engineers have narrowly surveyed the place, they are to make their report to the general, by acquainting him which part they judge the weakest, and where approaches may be made with most success. Their business is also to delineate the lines of circumvallation and contravallation, taking all the advantages of the ground; to mark out the trenches, places of arms, batteries, and lodgments, taking care that none of their works be flanked or discovered from the place. After making a faithful report to the general of what is a-doing, the engineers are to demand a sufficient number of workmen and utensils, and whatever else is necessary.
In Encyclopaedia Britannica or a Dictionary of Arts and Sciences (1771), Vol. 2, 497.
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Equations are Expressions of Arithmetical Computation, and properly have no place in Geometry, except as far as Quantities truly Geometrical (that is, Lines, Surfaces, Solids, and Proportions) may be said to be some equal to others. Multiplications, Divisions, and such sort of Computations, are newly received into Geometry, and that unwarily, and contrary to the first Design of this Science. For whosoever considers the Construction of a Problem by a right Line and a Circle, found out by the first Geometricians, will easily perceive that Geometry was invented that we might expeditiously avoid, by drawing Lines, the Tediousness of Computation. Therefore these two Sciences ought not to be confounded. The Ancients did so industriously distinguish them from one another, that they never introduced Arithmetical Terms into Geometry. And the Moderns, by confounding both, have lost the Simplicity in which all the Elegance of Geometry consists. Wherefore that is Arithmetically more simple which is determined by the more simple Equation, but that is Geometrically more simple which is determined by the more simple drawing of Lines; and in Geometry, that ought to be reckoned best which is geometrically most simple.
In 'On the Linear Construction of Equations', Universal Arithmetic (1769), Vol. 2, 470.
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Every arsenate has its corresponding phosphate, composed according to the same proportions, combined with the same amount of water of crystallization, and endowed with the same physical properties: in fact, the two series of salts differ in no respect, except that the radical of the acid in one series in phosphorus, while in the other it is arsenic.
The experimental clue he used forming his law of isomerism. Originally published in 'Om Förhållandet emellan chemiska sammansättningen och krystallformen hos Arseniksyrade och Phosphorsyrade Salter', (On the Relation between the Chemical Composition and Crystal Form of Salts of Arsenic and Phosphoric Acids), Kungliga Svenska vetenskapsakademiens handlingar (1821), 4. Translation as shown in Joseph William Mellor, A Comprehensive Treatise on Inorganic and Theoretical Chemistry (1922), Vol. 1, 652. A very similar translation (“the same physical properties” is replaced with “nearly equal solubilities in water and acids”) is in F. Szabadváry article on 'Eilhard Mitscherlich' in Charles Coulston Gillispie (ed.), Dictionary of Scientific Biography (1974), Vol. 9, 424; perhaps from J.R. Partington, A History of Chemistry, Vol. 4 (1964), 210.
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Every gambler stakes a certainty to gain an uncertainty, and yet he stakes a finite certainty against a finite uncertainty without acting unreasonably. … The uncertainty of gain is proportioned to the certainty of the stake, according to the proportion of chances of gain and loss, and if therefore there are as many chances on one side as on the other, the game is even.
In Blaise Pascal and C. Kegan Paul (trans.), 'Of The Need of Seeking Truth', The Thought of Blaise Pascal: Translated from the Text of M. Auguste Molinier (1905), 98.
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Experience is never at fault; it is only your judgment that is in error in promising itself such results from experience as are not caused by our experiments. For having given a beginning, what follows from it must necessarily be a natural development of such a beginning, unless it has been subject to a contrary influence, while, if it is affected by any contrary influence, the result which ought to follow from the aforesaid beginning will be found to partake of this contrary influence in a greater or less degree in proportion as the said influence is more or less powerful than the aforesaid beginning.
'Philosophy', in The Notebooks of Leonardo da Vinci, trans. E. MacCurdy (1938), Vol. 1, 70.
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For any two portions of fire, small or great, will exhibit the same ratio of solid to void; but the upward movement of the greater is quicker than that of the less, just as the downward movement of a mass of gold or lead, or of any other body endowed with weight, is quicker in proportion to its size.
Aristotle
On the Heavens, 309b, 11-5. In Jonathan Barnes (ed.), The Complete Works of Aristotle (1984), Vol. I, 505.
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Fortunately Nature herself seems to have prepared for us the means of supplying that want which arises from the impossibility of making certain experiments on living bodies. The different classes of animals exhibit almost all the possible combinations of organs: we find them united, two and two, three and three, and in all proportions; while at the same time it may be said that there is no organ of which some class or some genus is not deprived. A careful examination of the effects which result from these unions and privations is therefore sufficient to enable us to form probable conclusions respecting the nature and use of each organ, or form of organ. In the same manner we may proceed to ascertain the use of the different parts of the same organ, and to discover those which are essential, and separate them from those which are only accessory. It is sufficient to trace the organ through all the classes which possess it, and to examine what parts constantly exist, and what change is produced in the respective functions of the organ, by the absence of those parts which are wanting in certain classes.
Letter to Jean Claude Mertrud. In Lectures on Comparative Anatomy (1802), Vol. I, xxiii--xxiv.
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GRAVITATION, n. The tendency of all bodies to approach one another with a strength proportioned to the quantity of matter they contain—the quantity of matter they contain being ascertained by the strength of their tendency to approach one another. This is a lovely and edifying illustration of how science, having made A the proof of B, makes B the proof of A.
The Collected Works of Ambrose Bierce (1911), Vol. 7, The Devil's Dictionary,  123.
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Having been the discoverer of many splendid things, he is said to have asked his friends and relations that, after his death, they should place on his tomb a cylinder enclosing a sphere, writing on it the proportion of the containing solid to that which is contained.
Plutarch, Life of Marcellus, 17.12. Trans. R. W. Sharples.
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I am further inclined to think, that when our views are sufficiently extended, to enable us to reason with precision concerning the proportions of elementary atoms, we shall find the arithmetical relation alone will not be sufficient to explain their mutual action, and that we shall be obliged to acquire a geometric conception of their relative arrangement in all three dimensions of solid extension.
Paper. Read to the Royal Society (28 Jan 1808), in 'On Super-acid and Sub-acid salts', Philosophical Transactions of the Royal Society of London, (1808), 98, 101.
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I am particularly concerned to determine the probability of causes and results, as exhibited in events that occur in large numbers, and to investigate the laws according to which that probability approaches a limit in proportion to the repetition of events. That investigation deserves the attention of mathematicians because of the analysis required. It is primarily there that the approximation of formulas that are functions of large numbers has its most important applications. The investigation will benefit observers in identifying the mean to be chosen among the results of their observations and the probability of the errors still to be apprehended. Lastly, the investigation is one that deserves the attention of philosophers in showing how in the final analysis there is a regularity underlying the very things that seem to us to pertain entirely to chance, and in unveiling the hidden but constant causes on which that regularity depends. It is on the regularity of the main outcomes of events taken in large numbers that various institutions depend, such as annuities, tontines, and insurance policies. Questions about those subjects, as well as about inoculation with vaccine and decisions of electoral assemblies, present no further difficulty in the light of my theory. I limit myself here to resolving the most general of them, but the importance of these concerns in civil life, the moral considerations that complicate them, and the voluminous data that they presuppose require a separate work.
Philosophical Essay on Probabilities (1825), trans. Andrew I. Dale (1995), Introduction.
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I do not intend to go deeply into the question how far mathematical studies, as the representatives of conscious logical reasoning, should take a more important place in school education. But it is, in reality, one of the questions of the day. In proportion as the range of science extends, its system and organization must be improved, and it must inevitably come about that individual students will find themselves compelled to go through a stricter course of training than grammar is in a position to supply. What strikes me in my own experience with students who pass from our classical schools to scientific and medical studies, is first, a certain laxity in the application of strictly universal laws. The grammatical rules, in which they have been exercised, are for the most part followed by long lists of exceptions; accordingly they are not in the habit of relying implicitly on the certainty of a legitimate deduction from a strictly universal law. Secondly, I find them for the most part too much inclined to trust to authority, even in cases where they might form an independent judgment. In fact, in philological studies, inasmuch as it is seldom possible to take in the whole of the premises at a glance, and inasmuch as the decision of disputed questions often depends on an aesthetic feeling for beauty of expression, or for the genius of the language, attainable only by long training, it must often happen that the student is referred to authorities even by the best teachers. Both faults are traceable to certain indolence and vagueness of thought, the sad effects of which are not confined to subsequent scientific studies. But certainly the best remedy for both is to be found in mathematics, where there is absolute certainty in the reasoning, and no authority is recognized but that of one’s own intelligence.
In 'On the Relation of Natural Science to Science in general', Popular Lectures on Scientific Subjects, translated by E. Atkinson (1900), 25-26.
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I do not … reject the use of statistics in medicine, but I condemn not trying to get beyond them and believing in statistics as the foundation of medical science. … Statistics … apply only to cases in which the cause of the facts observed is still [uncertain or] indeterminate. … There will always be some indeterminism … in all the sciences, and more in medicine than in any other. But man’s intellectual conquest consists in lessening and driving back indeterminism in proportion as he gains ground for determinism by the help of the experimental method..
From An Introduction to the Study of Experimental Medicine (1865), as translated by Henry Copley Greene (1957), 138-140.
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I don’t know anything about mathematics; can’t even do proportion. But I can hire all the good mathematicians I need for fifteen dollars a week.
As quoted in French Strother, 'The Modern Profession of Inventing', World's Work and Play (Jul 1905), 6, No. 32, 187.
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I find in the domestic duck that the bones of the wing weigh less and the bones of the leg more, in proportion to the whole skeleton, than do the same bones in the wild duck; and this change may be safely attributed to the domestic duck flying much less, and walking more, than its wild parents.
From On the Origin of Species by Means of Natural Selection; or, The Preservation of Favoured Races in the Struggle for Life (1861), 17.
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I learned a lot of different things from different schools. MIT is a very good place…. It has developed for itself a spirit, so that every member of the whole place thinks that it’s the most wonderful place in the world—it’s the center, somehow, of scientific and technological development in the United States, if not the world … and while you don’t get a good sense of proportion there, you do get an excellent sense of being with it and in it, and having motivation and desire to keep on…
From Surely You’re Joking, Mr. Feynman!: Adventures of a Curious Character (1985), 51.
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I took a good clear piece of Cork and with a Pen-knife sharpen'd as keen as a Razor, I cut a piece of it off, and thereby left the surface of it exceeding smooth, then examining it very diligently with a Microscope, me thought I could perceive it to appear a little porous; but I could not so plainly distinguish them, as to be sure that they were pores, much less what Figure they were of: But judging from the lightness and yielding quality of the Cork, that certainly the texture could not be so curious, but that possibly, if I could use some further diligence, I might find it to be discernable with a Microscope, I with the same sharp Penknife, cut off from the former smooth surface an exceeding thin piece of it with a deep plano-convex Glass, I could exceedingly plainly perceive it to be all perforated and porous, much like a Honey-comb, but that the pores of it were not regular; yet it was not unlike a Honey-comb in these particulars.
First, in that it had a very little solid substance, in comparison of the empty cavity that was contain'd between, ... for the Interstitia or walls (as I may so call them) or partitions of those pores were neer as thin in proportion to their pores as those thin films of Wax in a Honey-comb (which enclose and constitute the sexangular cells) are to theirs.
Next, in that these pores, or cells, were not very deep, but constituted of a great many little Boxes, separated out of one continued long pore, by certain Diaphragms...
I no sooner discerned these (which were indeed the first microscopical pores I ever saw, and perhaps, that were ever seen, for I had not met with any Writer or Person, that had made any mention of them before this) but me thought I had with the discovery of them, presently hinted to me the true and intelligible reason of all the Phænomena of Cork.
Micrographia, or some Physiological Descriptions of Minute Bodies made by Magnifying Glasses with Observations and Inquiries thereupon (1665), 112-6.
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I use the word “attraction” here in a general sense for any endeavor whatever of bodies to approach one another, whether that endeavor occurs as a result of the action of the bodies either drawn toward one other or acting on one another by means of spirits emitted or whether it arises from the action of aether or of air or of any medium whatsoever—whether corporeal or incorporeal—in any way impelling toward one another the bodies floating therein. I use the word “impulse” in the same general sense, considering in this treatise not the species of forces and their physical qualities but their quantities and mathematical proportions, as I have explained in the definitions.
The Principia: Mathematical Principles of Natural Philosophy (1687), 3rd edition (1726), trans. I. Bernard Cohen and Anne Whitman (1999), Book I, Section II, Scholium, 588.
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I will not now discuss the Controversie betwixt some of the Modern Atomists, and the Cartesians; the former of whom think, that betwixt the Earth and the Stars, and betwixt these themselves there are vast Tracts of Space that are empty, save where the beams of Light do pass through them; and the later of whom tell us, that the Intervals betwixt the Stars and Planets (among which the Earth may perhaps be reckon'd) are perfectly fill'd, but by a Matter far subtiler than our Air, which some call Celestial, and others Æther. I shall not, I say, engage in this controversie, but thus much seems evident, That If there be such a Celestial Matter, it must ' make up far the Greatest part of the Universe known to us. For the Interstellar part of the world (If I may so stile it) bears so very great a proportion to the Globes, and their Atmospheres too, (If other Stars have any as well as the Earth,) that It Is almost incomparably Greater in respect of them, than all our Atmosphere is in respect of the Clouds, not to make the comparison between the Sea and the Fishes that swim in it.
A Continuation of New Experiments Physico-Mechanical, Touching the Spring and Weight of the Air, and their Effects (1669), 127.
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If I had been taught from my youth all the truths of which I have since sought out demonstrations, and had thus learned them without labour, I should never, perhaps, have known any beyond these; at least, I should never have acquired the habit and the facility which I think I possess in always discovering new truths in proportion as I give myself to the search.
In Discours de la Méthode (1637). In English from John Veitch (trans.), A Discourse on Method (1912), 57.
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If one of these elements, heat, becomes predominant in any body whatsoever, it destroys and dissolves all the others with its violence. …Again if too much moisture enters the channels of a body, and thus introduces disproportion, the other elements, adulterated by the liquid, are impaired, and the virtues of the mixture dissolved. This defect, in turn, may arise from the cooling properties of moist winds and breezes blowing upon the body. In the same way, increase or diminution of the proportion of air or of the earthy which is natural to the body may enfeeble the other elements.
Vitruvius
In De Architectura, Book 1, Chap 4, Sec. 6. As translated in Morris Hicky Morgan (trans.), Vitruvius: The Ten Books on Architecture (1914), 18-19.
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If this fire determined by the sun, be received on the blackest known bodies, its heat will be long retain'd therein; and hence such bodies are the soonest and the strongest heated by the flame fire, as also the quickest dried, after having been moisten'd with water; and it may be added, that they also burn by much the readiest: all which points are confirm'd by daily observations. Let a piece of cloth be hung in the air, open to the sun, one part of it dyed black, another part of a white colour, others of scarlet, and diverse other colours; the black part will always be found to heat the most, and the quickest of all; and the others will each be found to heat more slowly, by how much they reflect the rays more strongly to the eye; thus the white will warm the slowest of them all, and next to that the red, and so of the rest in proportion, as their colour is brighter or weaker.
A New Method of Chemistry, 2nd edition (1741), 262.
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Imagination is more robust in proportion as reasoning power is weak.
In The New Science (3rd ed., 1744), Book 1, Para. 185, as translated by Thomas Goddard Bergin and Max Harold Fisch, The New Science of Giambattista Vico (1948), 63.
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In a large proportion of cases treated by physicians the disease is cured by nature, not by them. In a lesser, but not a small proportion, the disease is cured by nature in spite of them.
…...
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In fact, Gentlemen, no geometry without arithmetic, no mechanics without geometry... you cannot count upon success, if your mind is not sufficiently exercised on the forms and demonstrations of geometry, on the theories and calculations of arithmetic ... In a word, the theory of proportions is for industrial teaching, what algebra is for the most elevated mathematical teaching.
... a l'ouverture du cours de mechanique industrielle á Metz (1827), 2-3, trans. Ivor Grattan-Guinness.
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In my work on Fossil Bones, I set myself the task of recognizing to which animals the fossilized remains which fill the surface strata of the earth belong. ... As a new sort of antiquarian, I had to learn to restore these memorials to past upheavals and, at the same time, to decipher their meaning. I had to collect and put together in their original order the fragments which made up these animals, to reconstruct the ancient creatures to which these fragments belonged, to create them once more with their proportions and characteristics, and finally to compare them to those alive today on the surface of the earth. This was an almost unknown art, which assumed a science hardly touched upon up until now, that of the laws which govern the coexistence of forms of the various parts in organic beings.
Discours sur les révolutions du globe, (Discourse on the Revolutions of the Surface of the Globe), originally the introduction to Recherches sur les ossemens fossiles des quadrupèdes (1812). Translated by Ian Johnston from the 1825 edition. Online at Vancouver Island University website.
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In Pure Mathematics, where all the various truths are necessarily connected with each other, (being all necessarily connected with those hypotheses which are the principles of the science), an arrangement is beautiful in proportion as the principles are few; and what we admire perhaps chiefly in the science, is the astonishing variety of consequences which may be demonstrably deduced from so small a number of premises.
In Elements of the Philosophy of the Human Mind (1827), Vol. 3, Chap. 1, Sec. 8, 186.
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In reality, I have sometimes thought that we do not go on sufficiently slowly in the removal of diseases, and that it would he better if we proceeded with less haste, and if more were often left, to Nature than is the practice now-a-days. It is a great mistake to suppose that Nature always stands in need of the assistance of Art. If that were the case, site would have made less provision for the safety of mankind than the preservation of the species demands; seeing that there is not the least proportion between the host of existing diseases and the powers possessed by man for their removal, even in those ages wherein the healing art was at the highest pitch, and most extensively cultivated.
As quoted by Gavin Milroy in 'On the Writings of Sydenham', The Lancet (14 Nov 1846), 524.
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In the beginning of the year 1665 I found the Method of approximating series & the Rule for reducing any dignity of any Bionomial into such a series. The same year in May I found the method of Tangents of Gregory & Slusius, & in November had the direct method of fluxions & the next year in January had the Theory of Colours & in May following I had entrance into ye inverse method of fluxions. And the same year I began to think of gravity extending to ye orb of the Moon & (having found out how to estimate the force with wch [a] globe revolving within a sphere presses the surface of the sphere) from Keplers rule of the periodic times of the Planets being in sesquialterate proportion of their distances from the center of their Orbs, I deduced that the forces wch keep the Planets in their Orbs must [be] reciprocally as the squares of their distances from the centers about wch they revolve: & thereby compared the force requisite to keep the Moon in her Orb with the force of gravity at the surface of the earth, & found them answer pretty nearly. All this was in the two plague years of 1665-1666. For in those days I was in the prime of my age for invention & minded Mathematicks & Philosophy more then than at any time since.
Quoted in Richard Westfall, Never at Rest: A Biography of Isaac Newton (1980), 143.
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In the process of natural selection, then, any device that can insert a higher proportion of certain genes into subsequent generations will come to characterize the species.
'The Morality of the Gene'.; Sociobiology: The New Synthesis (1975, 1980), 3.
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In the vestibule of the Manchester Town Hall are placed two life-sized marble statues facing each other. One of these is that of John Dalton … the other that of James Prescott Joule. … Thus honour is done to Manchester’s two greatest sons—to Dalton, the founder of modern Chemistry and of the Atomic Theory, and the laws of chemical-combining proportions; to Joule, the founder of modern Physics and the discoverer of the Law of Conservation of Energy. The one gave to the world the final and satisfactory proof … that in every kind of chemical change no loss of matter occurs; the other proved that in all the varied modes of physical change, no loss of energy takes place.
In John Dalton and the Rise of Modern Chemistry (1895), 7.
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In this generation, along with the dominating traits, the recessive ones also reappear, their individuality fully revealed, and they do so in the decisively expressed average proportion of 3:1, so that among each four plants of this generation three receive the dominating and one the recessive characteristic.
'Experiments on Plant Hybrids' (1865). In Curt Stern and Eva R. Sherwood (eds.), The Origin of Genetics: A Mendel Source Book (1966), 10.
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It follows from the supreme perfection of God, that in creating the universe has chosen the best possible plan, in which there is the greatest variety together with the greatest order; the best arranged ground, place, time; the most results produced in the most simple ways; the most of power, knowledge, happiness and goodness the creatures that the universe could permit. For since all the possibles in I understanding of God laid claim to existence in proportion to their perfections, the actual world, as the resultant of all these claims, must be the most perfect possible. And without this it would not be possible to give a reason why things have turned out so rather than otherwise.
The Principles of Nature and Grace (1714), The Philosophical Works of Leibnitz (1890), ed. G. M. Duncan, 213-4.
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It is a scale of proportions which makes the bad difficult and the good easy.
…...
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It is from this absolute indifference and tranquility of the mind, that mathematical speculations derive some of their most considerable advantages; because there is nothing to interest the imagination; because the judgment sits free and unbiased to examine the point. All proportions, every arrangement of quantity, is alike to the understanding, because the same truths result to it from all; from greater from lesser, from equality and inequality.
In On the Sublime and Beautiful, Part 3, sect. 2.
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It is natural for man to relate the units of distance by which he travels to the dimensions of the globe that he inhabits. Thus, in moving about the earth, he may know by the simple denomination of distance its proportion to the whole circuit of the earth. This has the further advantage of making nautical and celestial measurements correspond. The navigator often needs to determine, one from the other, the distance he has traversed from the celestial arc lying between the zeniths at his point of departure and at his destination. It is important, therefore, that one of these magnitudes should be the expression of the other, with no difference except in the units. But to that end, the fundamental linear unit must be an aliquot part of the terrestrial meridian. ... Thus, the choice of the metre was reduced to that of the unity of angles.
Lecture at the École Normale to the Year III (Apr 1795), Oeuvres Completes de Laplace (1878-1912), Vol. 14, 141. In Charles Coulston Gillispie, Dictionary of Scientific Biography (1978), Vol. 15, 335.
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It is not failure but success that is forcing man off this earth. It is not sickness but the triumph of health... Our capacity to survive has expanded beyond the capacity of Earth to support us. The pains we are feeling are growing pains. We can solve growth problems in direct proportion to our capacity to find new worlds... If man stays on Earth, his extinction is sure even if he lasts till the sun expands and destroys him... It is no longer reasonable to assume that the meaning of life lies on this earth alone. If Earth is all there is for man, we are reaching the foreseeable end of man.
…...
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It is very remarkable that while the words Eternal, Eternity, Forever, are constantly in our mouths, and applied without hesitation, we yet experience considerable difficulty in contemplating any definite term which bears a very large proportion to the brief cycles of our petty chronicles. There are many minds that would not for an instant doubt the God of Nature to have existed from all Eternity, and would yet reject as preposterous the idea of going back a million of years in the History of His Works. Yet what is a million, or a million million, of solar revolutions to an Eternity?
Memoir on the Geology of Central France (1827), 165.
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It seems probable to me that God, in the beginning, formed matter in solid, massy, hard, impenetrable, moveable particles, of such sizes and figures, and with such other properties, and in such proportions to space, as most conduced to the end for which He formed them; and that these primitive particles, being solids, are incomparably harder than any porous bodies compounded of them, even so very hard as never to wear or break in pieces; no ordinary power being able to divide what God had made one in the first creation.
From Opticks (1704, 2nd ed., 1718), 375-376.
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Law 2: A change in motion is proportional to the motive force impressed and takes place along the straight line in which that force is impressed.
The Principia: Mathematical Principles of Natural Philosophy (1687), 3rd edition (1726), trans. I. Bernard Cohen and Anne Whitman (1999), Axioms, or Laws of Motion, Law 2, 416.
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Man has become a superman ... because he not only disposes of innate, physical forces, but because he is in command ... of latent forces in nature he can put them to his service. ... But the essential fact we must surely all feel in our hearts ... is that we are becoming inhuman in proportion as we become supermen.
Speech (4 Nov 1954) upon receiving the Nobel Peace Prize. In 'Excerpts From the Nobel Prize Address Dr. Schweitzer in Oslo', New York Times (5 Nov 1954), 4.
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Mathematics has beauties of its own—a symmetry and proportion in its results, a lack of superfluity, an exact adaptation of means to ends, which is exceedingly remarkable and to be found only in the works of the greatest beauty. … When this subject is properly and concretely presented, the mental emotion should be that of enjoyment of beauty, not that of repulsion from the ugly and the unpleasant.
In The Teaching of Mathematics in the Elementary and the Secondary School (1906), 44-45.
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Mathematics is a dangerous profession; an appreciable proportion of us go mad.
In A Mathematician’s Miscellany (1953), reissued as Béla Bollobás (ed.), Littlewood’s Miscellany (1986), 104.
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Men are wise in proportion, not to their experience, but to their capacity for experience.
In 'Maxims for Revolutionists: Experience', in Man and Superman (1903), 239.
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Men become civilized, not in proportion to their willingness to believe, but in proportion to their readiness to doubt.
…...
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Men go into space to see whether it is the kind of place where other men, and their families and their children, can eventually follow them. A disturbingly high proportion of the intelligent young are discontented because they find the life before them intolerably confining. The moon offers a new frontier. It is as simple and splendid as that.
Magazine
Editorial on the moon landing, The Economist (1969).
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Mr. Dalton's aspect and manner were repulsive. There was no gracefulness belonging to him. His voice was harsh and brawling; his gait stiff and awkward; his style of writing and conversation dry and almost crabbed. In person he was tall, bony, and slender. He never could learn to swim: on investigating this circumstance he found that his spec. grav. as a mass was greater than that of water; and he mentioned this in his lectures on natural philosophy in illustration of the capability of different persons for attaining the art of swimming. Independence and simplicity of manner and originality were his best qualities. Though in comparatively humble circumstances he maintained the dignity of the philosophical character. As the first distinct promulgator of the doctrine that the elements of bodies unite in definite proportions to form chemical compounds, he has acquired an undying fame.
Dr John Davy's (brother of Humphry Davy) impressions of Dalton written in c.1830-31 in Malta.
John Davy
Quoted in W. C. Henry, Memoirs of the Life and Scientific Researches of John Dalton (1854), 217-8.
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No creature is too bulky or formidable for man's destructive energies—none too minute and insignificant for his keen detection and skill of capture. It was ordained from the beginning that we should be the masters and subduers of all inferior animals. Let us remember, however, that we ourselves, like the creatures we slay, subjugate, and modify, are the results of the same Almighty creative will—temporary sojourners here, and co-tenants with the worm and the whale of one small planet. In the exercise, therefore, of those superior powers that have been intrusted to us, let us ever bear in mind that our responsibilities are heightened in proportion.
Lecture to the London Society of Arts, 'The Raw Materials of the Animal Kingdom', collected in Lectures on the Results of the Great Exhibition of 1851' (1852), 131.
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Nowadays everyone knows that the US is the world’s biggest polluter, and that with only one 20th of the world’s population it produces a quarter of its greenhouse gas emissions. But the US government, in an abdication of leadership of epic proportions, is refusing to take the problem seriously. … Emissions from the US are up 14% on those in 1990 and are projected to rise by a further 12% over the next decade.
In 'Global Warming is Now a Weapon of Mass Destruction', The Guardian (28 Jul 2003).
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On coming down the stairs at dinner Tris [Trismegistus = Frankland] who walked before me seemed impressed by a mechanical impulse which impelled him along the corridor with a fervid velocity. On reaching the stair bottom I discovered the cause of the attraction. Miss Edmondson, like a pure planet, had checked his gravitating tendencies and lo! He stood radiant with smiles dropping joysparkes from his eyes as he clasped her hand. His countenance became a transparency through which the full proportions of his soul shone manifest; his blood tingled from his eyebrows to his finger ends, and wealthy with rich emotions his face became the avenue of what he felt.
Journals of John Tyndall, 18 Jan 1848. Royal Institution Archives.
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Our commercial and mercantile law was no sudden invention. It was not the work of a day, or of one set of minds… In the incipient, the early existence of this system, a single maxim obtained force, others succeeded; one rule of right formed a nucleus around which other kindred rules might cling; the necessities of trade originated customs, customs ripened into law; a few feeble decisions of courts laid the foundation for others; the wisdom and experience of each succeeding generation improved upon the wisdom and experience of generations that were past; and thus the edifice arose, perfect in its parts, beautiful in its proportions.
From biographical preface by T. Bigelow to Austin Abbott (ed.), Official Report of the Trial of Henry Ward Beecher (1875), Vol. 1, xi-xii.
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Our delight in any particular study, art, or science rises and improves in proportion to the application which we bestow upon it. Thus, what was at first an exercise becomes at length an entertainment.
In The Spectator (2 Aug 1712), No. 447, collected in The Spectator (9th ed., 1728), Vol. 6, 225.
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Physiology is the basis of all medical improvement and in precise proportion as our survey of it becomes more accurate and extended, it is rendered more solid.
In 'An Inquiry, Analogical and Experimental, into the Different Electrical conditions of Arterial and Venous Blood', New Orleans Medical and Surgical Journal (1853-4), 10, 584-602 & 738-757. As cited in George B. Roth, 'Dr. John Gorrie—Inventor of Artificial Ice and Mechanical Refrigeration', The Scientific Monthly (May 1936) 42 No. 5, 464-469.
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Saturated with that speculative spirit then pervading the Greek mind, he [Pythagoras] endeavoured to discover some principle of homogeneity in the universe. Before him, the philosophers of the Ionic school had sought it in the matter of things; Pythagoras looked for it in the structure of things. He observed the various numerical relations or analogies between numbers and the phenomena of the universe. Being convinced that it was in numbers and their relations that he was to find the foundation to true philosophy, he proceeded to trace the origin of all things to numbers. Thus he observed that musical strings of equal lengths stretched by weights having the proportion of 1/2, 2/3, 3/4, produced intervals which were an octave, a fifth and a fourth. Harmony, therefore, depends on musical proportion; it is nothing but a mysterious numerical relation. Where harmony is, there are numbers. Hence the order and beauty of the universe have their origin in numbers. There are seven intervals in the musical scale, and also seven planets crossing the heavens. The same numerical relations which underlie the former must underlie the latter. But where number is, there is harmony. Hence his spiritual ear discerned in the planetary motions a wonderful “Harmony of spheres.”
In History of Mathematics (1893), 67.
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Spherical space is not very easy to imagine. We have to think of the properties of the surface of a sphere—the two-dimensional case—and try to conceive something similar applied to three-dimensional space. Stationing ourselves at a point let us draw a series of spheres of successively greater radii. The surface of a sphere of radius r should be proportional to r2; but in spherical space the areas of the more distant spheres begin to fall below the proper proportion. There is not so much room out there as we expected to find. Ultimately we reach a sphere of biggest possible area, and beyond it the areas begin to decrease. The last sphere of all shrinks to a point—our antipodes. Is there nothing beyond this? Is there a kind of boundary there? There is nothing beyond and yet there is no boundary. On the earth’s surface there is nothing beyond our own antipodes but there is no boundary there
In Space, Time and Gravitation: An Outline of the General Relativity Theory (1920, 1921), 158-159.
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Statistical accounts are to be referred to as a dictionary by men of riper years, and by young men as a grammar, to teach them the relations and proportions of different statistical subjects, and to imprint them on the mind at a time when the memory is capable of being impressed in a lasting and durable manner, thereby laying the foundation for accurate and valuable knowledge.
In The Statistical Breviary: Shewing, on a Principle Entirely New, the Resources of Every State and Kingdom in Europe (1801), 5-6.
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Suppose then I want to give myself a little training in the art of reasoning; suppose I want to get out of the region of conjecture and probability, free myself from the difficult task of weighing evidence, and putting instances together to arrive at general propositions, and simply desire to know how to deal with my general propositions when I get them, and how to deduce right inferences from them; it is clear that I shall obtain this sort of discipline best in those departments of thought in which the first principles are unquestionably true. For in all our thinking, if we come to erroneous conclusions, we come to them either by accepting false premises to start with—in which case our reasoning, however good, will not save us from error; or by reasoning badly, in which case the data we start from may be perfectly sound, and yet our conclusions may be false. But in the mathematical or pure sciences,—geometry, arithmetic, algebra, trigonometry, the calculus of variations or of curves,— we know at least that there is not, and cannot be, error in our first principles, and we may therefore fasten our whole attention upon the processes. As mere exercises in logic, therefore, these sciences, based as they all are on primary truths relating to space and number, have always been supposed to furnish the most exact discipline. When Plato wrote over the portal of his school. “Let no one ignorant of geometry enter here,” he did not mean that questions relating to lines and surfaces would be discussed by his disciples. On the contrary, the topics to which he directed their attention were some of the deepest problems,— social, political, moral,—on which the mind could exercise itself. Plato and his followers tried to think out together conclusions respecting the being, the duty, and the destiny of man, and the relation in which he stood to the gods and to the unseen world. What had geometry to do with these things? Simply this: That a man whose mind has not undergone a rigorous training in systematic thinking, and in the art of drawing legitimate inferences from premises, was unfitted to enter on the discussion of these high topics; and that the sort of logical discipline which he needed was most likely to be obtained from geometry—the only mathematical science which in Plato’s time had been formulated and reduced to a system. And we in this country [England] have long acted on the same principle. Our future lawyers, clergy, and statesmen are expected at the University to learn a good deal about curves, and angles, and numbers and proportions; not because these subjects have the smallest relation to the needs of their lives, but because in the very act of learning them they are likely to acquire that habit of steadfast and accurate thinking, which is indispensable to success in all the pursuits of life.
In Lectures on Teaching (1906), 891-92.
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Taking … the mathematical faculty, probably fewer than one in a hundred really possess it, the great bulk of the population having no natural ability for the study, or feeling the slightest interest in it*. And if we attempt to measure the amount of variation in the faculty itself between a first-class mathematician and the ordinary run of people who find any kind of calculation confusing and altogether devoid of interest, it is probable that the former could not be estimated at less than a hundred times the latter, and perhaps a thousand times would more nearly measure the difference between them.
[* This is the estimate furnished me by two mathematical masters in one of our great public schools of the proportion of boys who have any special taste or capacity for mathematical studies. Many more, of course, can be drilled into a fair knowledge of elementary mathematics, but only this small proportion possess the natural faculty which renders it possible for them ever to rank high as mathematicians, to take any pleasure in it, or to do any original mathematical work.]
In Darwinism, chap. 15.
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The 31th of May, I perceived in the same water more of those Animals, as also some that were somewhat bigger. And I imagine, that [ten hundred thousand] of these little Creatures do not equal an ordinary grain of Sand in bigness: And comparing them with a Cheese-mite (which may be seen to move with the naked eye) I make the proportion of one of these small Water-creatures to a Cheese-mite, to be like that of a Bee to a Horse: For, the circumference of one of these little Animals in water, is not so big as the thickness of a hair in a Cheese-mite.
Letter to H. Oldenburg, 9 Oct 1676. In The Collected Letters of Antoni van Leeuwenhoek (1957), Vol. 2, 75.
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The absolute extent of land in the Archipelago is not greater than that contained by Western Europe from Hungary to Spain; but, owing to the manner in which the land is broken up and divided, the variety of its productions is rather in proportion to the immense surface over which the islands are spread, than to the quantity of land which they contain.
Malay Archipelago
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The amount of knowledge which we can justify from evidence directly available to us can never be large. The overwhelming proportion of our factual beliefs continue therefore to be held at second hand through trusting others, and in the great majority of cases our trust is placed in the authority of comparatively few people of widely acknowledged standing.
Personal Knowledge (1958), 208.
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The body of man has in itself blood, phlegm, yellow bile and black bile; these make up the nature of this body, and through these he feels pain or enjoys health. Now he enjoys the most perfect health when these elements are duly proportioned to one another in respect of compounding, power and bulk, and when they are perfectly mingled.
Nature of Man, in Hippocrates, trans. W. H. S. Jones (1931), Vol. 4, II.
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The discovery of the laws of definite proportions is one of the most important and wonderful among the great and brilliant achievements of modern chemistry. It is sufficient of itself to convince any reasoning mind, that order and system pervade the universe, and that the minutest atoms of matter, and the vast orbs that move round the heavens are equally under the control of the invariable laws of the creator.
Elements of Chemistry (1845), 84.
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The elegance of a mathematical theorem is directly proportional to the number of independent ideas one can see in the theorem and inversely proportional to the effort it takes to see them.
In Mathematical Discovery: On Understanding, Learning, and Teaching Problem Solving (1981). As cited, with no more details, in Yi Ma, An Invitation to 3-D Vision (2004), 228.
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The extraordinary development of mathematics in the last century is quite unparalleled in the long history of this most ancient of sciences. Not only have those branches of mathematics which were taken over from the eighteenth century steadily grown, but entirely new ones have sprung up in almost bewildering profusion, and many of them have promptly assumed proportions of vast extent.
In The History of Mathematics in the Nineteenth Century', Congress of Arts and Sciences (1905), Vol. 1, 474. As cited and wuoted in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 110.
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The extraordinary development of modern science may be her undoing. Specialism, now a necessity, has fragmented the specialities themselves in a way that makes the outlook hazardous. The workers lose all sense of proportion in a maze of minutiae.
'The Old Humanities and the New Science' (1919). In G. L. Keynes (ed.), Selected Writings of Sir William Osler (1951), 27.
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The faculty for remembering is not diminished in proportion to what one has learnt, just as little as the number of moulds in which you cast sand lessens its capacity for being cast in new moulds.
Religion: a Dialogue, and Other Essays (1890), 99.
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The faith of scientists in the power and truth of mathematics is so implicit that their work has gradually become less and less observation, and more and more calculation. The promiscuous collection and tabulation of data have given way to a process of assigning possible meanings, merely supposed real entities, to mathematical terms, working out the logical results, and then staging certain crucial experiments to check the hypothesis against the actual empirical results. But the facts which are accepted by virtue of these tests are not actually observed at all. With the advance of mathematical technique in physics, the tangible results of experiment have become less and less spectacular; on the other hand, their significance has grown in inverse proportion. The men in the laboratory have departed so far from the old forms of experimentation—typified by Galileo's weights and Franklin's kite—that they cannot be said to observe the actual objects of their curiosity at all; instead, they are watching index needles, revolving drums, and sensitive plates. No psychology of 'association' of sense-experiences can relate these data to the objects they signify, for in most cases the objects have never been experienced. Observation has become almost entirely indirect; and readings take the place of genuine witness.
Philosophy in a New Key; A Study in Inverse the Symbolism of Reason, Rite, and Art (1942), 19-20.
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The farther researches we make into this admirable scene of things, the more beauty and harmony we see in them: And the stronger and clearer convictions they give us, of the being, power and wisdom of the divine Architect, who has made all things to concur with a wonderful conformity, in carrying on, by various and innumerable combinations of matter, such a circulation of causes, and effects, as was necessary to the great ends of nature. And since we are assured that the all-wise Creator has observed the most exact proportions, of number, weight and measure, in the make of all things; the most likely way therefore, to get any insight into the nature of those parts of the creation, which come within our observation, must in all reason be to number, weigh and measure. And we have much encouragement to pursue this method, of searching into the nature of things, from the great success that has attended any attempts of this kind.
Vegetable Staticks (1727), xxxi.
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The House is composed of very good men, not shining, but honest and reasonably well-informed, and in time will be found to improve, and not much inferior in eloquence, science, and dignity, to the British Commons. They are patriotic enough, and I believe there are more stupid (as well as more shining) people in the latter, in proportion.
Letter to George Richard Minot (27 May 1789). Quoted in Set Ames (Ed.) Works of Fisher Ames (1854), Vol. 1, 45.
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The interior parts of the earth and its internal depths are a region totally impervious to the eye of mortal man, and can least of all be approached by those ordinary paths of hypothesis adopted by naturalists and geologists. The region designed for the existence of man, and of every other creature endowed with organic life, as well as the sphere opened to the perception of man's senses, is confined to a limited space between the upper and lower parts of the earth, exceedingly small in proportion to the diameter, or even semi-diameter of the earth, and forming only the exterior surface, or outer skin, of the great body of the earth.
In Friedrich von Schlegel and James Burton Robertson (trans.), The Philosophy of History (1835), 20.
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The main species of beauty are orderly arrangement, proportion, and definiteness; and these are especially manifested by the mathematical sciences.
Aristotle
In Metaphysics, 13-1078a-b, as translated by Hugh Tredennick (1933). Also seen translated as, “The mathematical sciences particularly exhibit order, symmetry, and limitation; and these are the greatest forms of the beautiful.”
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The man who proportions the several parts of a mill, uses the same scientific principles [mechanics], as if he had the power of constructing an universe; but as he cannot give to matter that invisible agency, by which all the component parts of the immense machine of the universe have influence upon each other, and set in motional unison together without any apparent contact, and to which man has given the name of attraction, gravitation, and repulsion, he supplies the place of that agency by the humble imitation of teeth and cogs. All the parts of man’s microcosm must visibly touch.
In The Age of Reason: Being an Investigation of True and Fabulous Theology (27 Jan O.S. 1794), 42-43.
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The mathematics of cooperation of men and tools is interesting. Separated men trying their individual experiments contribute in proportion to their numbers and their work may be called mathematically additive. The effect of a single piece of apparatus given to one man is also additive only, but when a group of men are cooperating, as distinct from merely operating, their work raises with some higher power of the number than the first power. It approaches the square for two men and the cube for three. Two men cooperating with two different pieces of apparatus, say a special furnace and a pyrometer or a hydraulic press and new chemical substances, are more powerful than their arithmetical sum. These facts doubtless assist as assets of a research laboratory.
Quoted from a speech delivered at the fiftieth anniversary of granting of M.I.T's charter, in Guy Suits, 'Willis Rodney Whitney', National Academy of Sciences, Biographical Memoirs (1960), 352.
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The most convincing proof of the conversion of heat into living force [vis viva] has been derived from my experiments with the electro-magnetic engine, a machine composed of magnets and bars of iron set in motion by an electrical battery. I have proved by actual experiment that, in exact proportion to the force with which this machine works, heat is abstracted from the electrical battery. You see, therefore, that living force may be converted into heat, and that heat may be converted into living force, or its equivalent attraction through space.
'On Matter, Living Force, and Heat' (1847). In The Scientific Papers of James Prescott Joule (1884), Vol. 1, 270-1.
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The name of medicine is thought to have been given from 'moderation', modus, that is, from a due proportion, which advises that things be done not to excess, but 'little by little', paulatim. For nature is pained by surfeit but rejoices in moderation. Whence also those who take drugs and antidotes constantly, or to the point of saturation, are sorely vexed, for every immoderation brings not health but danger.
Etymologies [c.600], Book IV, chapter 2, quoted in E. Grant (ed.), A Source Book in Medieval Science (1974), trans. W. D. Sharpe (1964), 701.
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The opinion I formed from attentive observation of the facts and phenomena, is as follows. When ice, for example, or any other solid substance, is changing into a fluid by heat, I am of opinion that it receives a much greater quantity of heat than that what is perceptible in it immediately after by the thermometer. A great quantity of heat enters into it, on this occasion, without making it apparently warmer, when tried by that instrument. This heat, however, must be thrown into it, in order to give it the form of a fluid; and I affirm, that this great addition of heat is the principal, and most immediate cause of the fluidity induced. And, on the other hand, when we deprive such a body of its fluidity again, by a diminution of its heat, a very great quantity of heat comes out of it, while it is assuming a solid form, the loss of which heat is not to be perceived by the common manner of using the thermometer. The apparent heat of the body, as measured by that instrument, is not diminished, or not in proportion to the loss of heat which the body actually gives out on this occasion; and it appears from a number of facts, that the state of solidity cannot be induced without the abstraction of this great quantity of heat. And this confirms the opinion, that this quantity of heat, absorbed, and, as it were, concealed in the composition of fluids, is the most necessary and immediate cause of their fluidity.
Lectures on the Elements of Chemistry, delivered in the University of Edinburgh (1803), Vol. I, 116-7.
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The other book you may have heard of and perhaps read, but it is not one perusal which will enable any man to appreciate it. I have read it through five or six times, each time with increasing admiration. It will live as long as the ‘Principia’ of Newton. It shows that nature is, as I before remarked to you, a study that yields to none in grandeur and immensity. The cycles of astronomy or even the periods of geology will alone enable us to appreciate the vast depths of time we have to contemplate in the endeavour to understand the slow growth of life upon the earth. The most intricate effects of the law of gravitation, the mutual disturbances of all the bodies of the solar system, are simplicity itself compared with the intricate relations and complicated struggle which have determined what forms of life shall exist and in what proportions. Mr. Darwin has given the world a new science, and his name should, in my opinion, stand above that of every philosopher of ancient or modem times. The force of admiration can no further go!!!
Letter to George Silk (1 Sep 1860), in My Life (1905), Vol. I, 372-373.
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The power of my [steam] engine rises in a geometrical proportion, while the consumption of fuel has only an arithmetical ratio; in such proportion that every time I added one fourth more to the consumption of fuel, the powers of the engine were doubled.
From 'On the Origin of Steam Boats and Steam Wagons', Thomas Cooper (ed.), The Emporium of Arts and Sciences (Feb 1814), 2, No. 2, 211-212.
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The primitive history of the species is all the more fully retained in its germ-history in proportion as the series of embryonic forms traversed is longer; and it is more accurately retained the less the mode of life of the recent forms differs from that of the earlier, and the less the peculiarities of the several embryonic states must be regarded as transferred from a later to an earlier period of life, or as acquired independently. (1864)
As translated and quoted in Ernst Haeckel and E. Ray Lankester (trans.) as epigraph for Chap. 13, The History of Creation (1886), Vol. 1, 406.
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The reduced variability of small populations is not always due to accidental gene loss, but sometimes to the fact that the entire population was started by a single pair or by a single fertilized female. These “founders” of the population carried with them only a very small proportion of the variability of the parent population. This “founder” principle sometimes explains even the uniformity of rather large populations, particularly if they are well isolated and near the borders of the range of the species.
Systematics and the Origin of Species: From the Viewpoint of a Zoologist (1942), 237.
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The risk of developing carcinoma of the lung increases steadily as the amount smoked increases. If the risk among non-smokers is taken as unity and the resulting ratios in the three age groups in which a large number of patients were interviewed (ages 45 to 74) are averaged, the relative risks become 6, 19, 26, 49, and 65 when the number of cigarettes smoked a day are 3, 10, 20, 35, and, say, 60—that is, the mid-points of each smoking group. In other words, on the admittedly speculative assumptions we have made, the risk seems to vary in approximately simple proportion with the amount smoked.
William Richard Shaboe Doll and Austin Bradford Hill (1897-1991 British medical statistician) 'Smoking and Carcinoma of the Lung', British Medical Journal, 1950, ii, 746.
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The science [of mathematics] has grown to such vast proportion that probably no living mathematician can claim to have achieved its mastery as a whole.
In An Introduction to Mathematics (1911), 262.
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The student should not lose any opportunity of exercising himself in numerical calculation and particularly in the use of logarithmic tables. His power of applying mathematics to questions of practical utility is in direct proportion to the facility which he possesses in computation.
In Study and Difficulties of Mathematics (1902), chap. 12.
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The two revolutions, I mean the annual revolutions of the declination and of the centre of the Earth, are not completely equal; that is the return of the declination to its original value is slightly ahead of the period of the centre. Hence it necessarily follows that the equinoxes and solstices seem to anticipate their timing, not because the sphere of the fixed stars moves to the east, but rather the equatorial circle moves to the west, being at an angle to the plane of the ecliptic in proportion to the declination of the axis of the terrestrial globe.
'Book Three. Chapter I. The Precession of the equinoxes and solstices', in Copernicus: On the Revolutions of the Heavenly Spheres (1543), trans. A. M. Duncan (1976), 141.
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The United States this week will commit its national pride, eight years of work and $24 billion of its fortune to showing the world it can still fulfill a dream. It will send three young men on a human adventure of mythological proportions with the whole of the civilized world invited to watch—for better or worse.
In 'Prestige of U.S. Rides on Apollo', Los Angeles Times (13 Jul 1969). As quoted and cited in Michael Collins, Carrying the Fire: An Astronaut’s Journey (2001), 315.
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The very bulk of scientific publications is itself delusive. It is of very unequal value; a large proportion of it, possibly as much as three-quarters, does not deserve to be published at all, and is only published for economic considerations which have nothing to do with the real interests of science.
The Social Function of Science (1939), 118.
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The weakness of men in comparison with women lies in the great intensity of their sexual desires. Man becomes dependent upon woman, and the more, the weaker and more sensual he becomes; and this just in proportion as he becomes neuropathic.
Psychopathia Sexualis: With Special Reference to Contrary Sexual Instinct: A Medico-Legal Study (1886), trans. Charles Gilbert Chaddock (1892), 14.
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There are … two fields for human thought and action—the actual and the possible, the realized and the real. In the actual, the tangible, the realized, the vast proportion of mankind abide. The great, region of the possible, whence all discovery, invention, creation proceed, and which is to the actual as a universe to a planet, is the chosen region of genius. As almost every thing which is now actual was once only possible, as our present facts and axioms were originally inventions or discoveries, it is, under God, to genius that we owe our present blessings. In the past, it created the present; in the present, it is creating the future.
In 'Genius', Wellman’s Miscellany (Dec 1871), 4, No. 6, 202.
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There is no area in our minds reserved for superstition, such as the Greeks had in their mythology; and superstition, under cover of an abstract vocabulary, has revenged itself by invading the entire realm of thought. Our science is like a store filled with the most subtle intellectual devices for solving the most complex problems, and yet we are almost incapable of applying the elementary principles of rational thought. In every sphere, we seem to have lost the very elements of intelligence: the ideas of limit, measure, degree, proportion, relation, comparison, contingency, interdependence, interrelation of means and ends. To keep to the social level, our political universe is peopled exclusively by myths and monsters; all it contains is absolutes and abstract entities. This is illustrated by all the words of our political and social vocabulary: nation, security, capitalism, communism, fascism, order, authority, property, democracy. We never use them in phrases such as: There is democracy to the extent that… or: There is capitalism in so far as… The use of expressions like “to the extent that” is beyond our intellectual capacity. Each of these words seems to represent for us an absolute reality, unaffected by conditions, or an absolute objective, independent of methods of action, or an absolute evil; and at the same time we make all these words mean, successively or simultaneously, anything whatsoever. Our lives are lived, in actual fact, among changing, varying realities, subject to the casual play of external necessities, and modifying themselves according to specific conditions within specific limits; and yet we act and strive and sacrifice ourselves and others by reference to fixed and isolated abstractions which cannot possibly be related either to one another or to any concrete facts. In this so-called age of technicians, the only battles we know how to fight are battles against windmills.
From 'The Power of Words', collected in Siân Miles (ed.), Simone Weil: An Anthology (2000), 222-223.
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There is no excellent beauty that hath not some strangeness in the proportions.
'Of Beauty.' Bacon's Essays (1880), Essay 43, 433.
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There is no sharp boundary line separating the reactions of the immune bodies from chemical processes between crystalloids, just as in nature there exists every stage between crystalloid and colloid. The nearer the colloid particle approximates to the normal electrolyte, the nearer its compounds must obviously come to conforming to the law of simple stoichiometric proportions, and the compounds themselves to simple chemical compounds. At this point, it should be recalled that Arrhenius has shown that the quantitative relationship between toxin and antitoxin is very similar to that between acid and base.
Landsteiner and Nicholas von Jagic, 'Uber Reaktionen anorganischer Kolloide und Immunkorper', Münchener medizinischer Wochenschrift (1904), 51, 1185-1189. Trans. Pauline M. H. Mazumdar.
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These Disciplines [mathematics] serve to inure and corroborate the Mind to a constant Diligence in Study; to undergo the Trouble of an attentive Meditation, and cheerfully contend with such Difficulties as lie in the Way. They wholly deliver us from a credulous Simplicity, most strongly fortify us against the Vanity of Scepticism, effectually restrain from a rash Presumption, most easily incline us to a due Assent, perfectly subject us to the Government of right Reason, and inspire us with Resolution to wrestle against the unjust Tyranny of false Prejudices. If the Fancy be unstable and fluctuating, it is to be poized by this Ballast, and steadied by this Anchor, if the Wit be blunt it is sharpened upon this Whetstone; if luxuriant it is pared by this Knife; if headstrong it is restrained by this Bridle; and if dull it is rouzed by this Spur. The Steps are guided by no Lamp more clearly through the dark Mazes of Nature, by no Thread more surely through the intricate Labyrinths of Philosophy, nor lastly is the Bottom of Truth sounded more happily by any other Line. I will not mention how plentiful a Stock of Knowledge the Mind is furnished from these, with what wholesome Food it is nourished, and what sincere Pleasure it enjoys. But if I speak farther, I shall neither be the only Person, nor the first, who affirms it; that while the Mind is abstracted and elevated from sensible Matter, distinctly views pure Forms, conceives the Beauty of Ideas, and investigates the Harmony of Proportions; the Manners themselves are sensibly corrected and improved, the Affections composed and rectified, the Fancy calmed and settled, and the Understanding raised and excited to more divine Contemplations. All which I might defend by Authority, and confirm by the Suffrages of the greatest Philosophers.
Prefatory Oration in Mathematical Lectures (1734), xxxi.
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These machines [used in the defense of the Syracusans against the Romans under Marcellus] he [Archimedes] had designed and contrived, not as matters of any importance, but as mere amusements in geometry; in compliance with king Hiero’s desire and request, some time before, that he should reduce to practice some part of his admirable speculation in science, and by accommodating the theoretic truth to sensation and ordinary use, bring it more within the appreciation of people in general. Eudoxus and Archytas had been the first originators of this far-famed and highly-prized art of mechanics, which they employed as an elegant illustration of geometrical truths, and as means of sustaining experimentally, to the satisfaction of the senses, conclusions too intricate for proof by words and diagrams. As, for example, to solve the problem, so often required in constructing geometrical figures, given the two extremes, to find the two mean lines of a proportion, both these mathematicians had recourse to the aid of instruments, adapting to their purpose certain curves and sections of lines. But what with Plato’s indignation at it, and his invectives against it as the mere corruption and annihilation of the one good of geometry,—which was thus shamefully turning its back upon the unembodied objects of pure intelligence to recur to sensation, and to ask help (not to be obtained without base supervisions and depravation) from matter; so it was that mechanics came to be separated from geometry, and, repudiated and neglected by philosophers, took its place as a military art.
Plutarch
In John Dryden (trans.), Life of Marcellus.
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Think of the image of the world in a convex mirror. ... A well-made convex mirror of moderate aperture represents the objects in front of it as apparently solid and in fixed positions behind its surface. But the images of the distant horizon and of the sun in the sky lie behind the mirror at a limited distance, equal to its focal length. Between these and the surface of the mirror are found the images of all the other objects before it, but the images are diminished and flattened in proportion to the distance of their objects from the mirror. ... Yet every straight line or plane in the outer world is represented by a straight line or plane in the image. The image of a man measuring with a rule a straight line from the mirror, would contract more and more the farther he went, but with his shrunken rule the man in the image would count out exactly the same results as in the outer world, all lines of sight in the mirror would be represented by straight lines of sight in the mirror. In short, I do not see how men in the mirror are to discover that their bodies are not rigid solids and their experiences good examples of the correctness of Euclidean axioms. But if they could look out upon our world as we look into theirs without overstepping the boundary, they must declare it to be a picture in a spherical mirror, and would speak of us just as we speak of them; and if two inhabitants of the different worlds could communicate with one another, neither, as far as I can see, would be able to convince the other that he had the true, the other the distorted, relation. Indeed I cannot see that such a question would have any meaning at all, so long as mechanical considerations are not mixed up with it.
In 'On the Origin and Significance of Geometrical Axioms,' Popular Scientific Lectures< Second Series (1881), 57-59. In Robert Édouard Moritz, Memorabilia Mathematica (1914), 357-358.
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This king [Sesostris] divided the land among all Egyptians so as to give each one a quadrangle of equal size and to draw from each his revenues, by imposing a tax to be levied yearly. But everyone from whose part the river tore anything away, had to go to him to notify what had happened; he then sent overseers who had to measure out how much the land had become smaller, in order that the owner might pay on what was left, in proportion to the entire tax imposed. In this way, it appears to me, geometry originated, which passed thence to Hellas.
Heroditus
(II. c. 109) As quoted in Florian Cajori, A History of Elementary Mathematics (1893), 10, footnoted to C.A. Bretschneider, Die Geometrie und die Geometer vor Eukides (1870). Note that the word geometry itself means “land measurement.”
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Thus far I have explained the phenomena of the heavens and of our sea by the force of gravity, but I have not yet assigned a cause to gravity. Indeed, this force arises from some cause that penetrates as far as the centers of the sun and planets without any diminution of its power to act, and that acts not in proportion to the quantity of the surfaces of the particles on which it acts (as mechanical causes are wont to do) but in proportion to the quantity of solid matter, and whose action is extended everywhere to immense distances, always decreasing as the squares of the distances.
The Principia: Mathematical Principles of Natural Philosophy (1687), 3rd edition (1726), trans. I. Bernard Cohen and Anne Whitman (1999), General Scholium, 943.
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To inquisitive minds like yours and mine the reflection that the quantity of human knowledge bears no proportion to the quantity of human ignorance must be in one view rather pleasing, viz., that though we are to live forever we may be continually amused and delighted with learning something new.
In letter to Dr. Ingenhouz. Quoted in Theodore Diller, Franklin's Contribution to Medicine (1912), 65. The source gives no specific cite for the letter, and Webmaster has found the quote in no other book checked, so authenticity is in question.
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True science and true religion are twin sisters, and the separation of either from the other is sure to prove the death of both. Science prospers exactly in proportion as it is religious; and religion flourishes in exact proportion to the scientific depth and firmness of its basis.
As quoted from the close of a recent lecture by Huxley in 'What Knowledge is of Most Worth'. Lectures in Education, by Herbert Spencer, delivered at the Royal Institution (1855). In The Westminster Review (Jul 1859), 22. Collected in Essays on Education and Kindred Subjects (1911), 41.
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We all remember the fairy tales of science in our infancy, which played with the supposition that large animals could jump in the proportion of small ones. If an elephant were as strong as a grasshopper, he could (I suppose) spring clean out of the Zoological Gardens and alight trumpeting upon Primrose Hill. If a whale could leap from the water like a trout, perhaps men might look up and see one soaring above Yarmouth like the winged island of Laputa.
In Manalive (1912), 26.
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We have now felled forest enough everywhere, in many districts far too much. Let us restore this one element of material life to its normal proportions, and devise means for maintaining the permanence of its relations to the fields, the meadows and the pastures, to the rain and the dews of heaven, to the springs and rivulets with which it waters down the earth.
From Man and Nature (1864), 328-329.
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We love to discover in the cosmos the geometrical forms that exist in the depths of our consciousness. The exactitude of the proportions of our monuments and the precision of our machines express a fundamental character of our mind. Geometry does not exist in the earthly world. It has originated in ourselves. The methods of nature are never so precise as those of man. We do not find in the universe the clearness and accuracy of our thought. We attempt, therefore, to abstract from the complexity of phenomena some simple systems whose components bear to one another certain relations susceptible of being described mathematically.
In Man the Unknown (1935), 8.
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We may now give the following more precise expression to our chief law of biogeny:— The evolution of the foetus (or ontogenesis) is a condensed and abbreviated recapitulation of the evolution of the stem (or phylogenesis); and this recapitulation is the more complete in proportion as the original development (or palingenesis) is preserved by a constant heredity; on the other hand, it becomes less complete in proportion as a varying adaptation to new conditions increases the disturbing factors in the development (or cenogenesis).
The Evolution of Man. Translated from the 5th edition of Anthropogenie by Joseph McCabe (1910), 8.
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We talk about our high standard of living in this country. What we have is a high standard of work. Usually the peaks of civilization have been periods when a large proportion of the population had time to live. I don’t think we’re doing this today. I think the people who could live are still spending their time and supplementary resources on making a living.
As quoted in Frances Glennon, 'Student and Teacher of Human Ways', Life (14 Sep 1959), 147.
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We think the heavens enjoy their spherical
Their round proportion, embracing all;
But yet their various and perplexed course,
Observed in divers ages, doth enforce
Men to find out so many eccentric parts,
Such diverse downright lines, such overthwarts,
As disproportion that pure form.
From poem, 'An Anatomy of the World: The First Anniversary', lines 251-257, as collected in The Poems of John Donne (1896), Vol. 2, 113.
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We’re going to see public attitudes [on climate change] switch not in proportion to scientific findings or graphs, but in proportion to the stories they hear, the people they know whose lives have been touched by climate change or some environmental calamity. That’s what really changed public opinion.
From interview with Mark Tercek, 'Q&A With Ramez Naam: Dialogues on the Environment', Huffington Post (1 Jul 2013).
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What vexes me most is, that my female friends, who could bear me very well a dozen years ago, have now forsaken me, although I am not so old in proportion to them as I formerly was: which I can prove by arithmetic, for then I was double their age, which now I am not.
In Letter (7 Feb 1736) to Alexander Pope, The Works of Jonathan Swift (1841), Vol. 2, 764.
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Whatever may happen to the latest theory of Dr. Einstein, his treatise represents a mathematical effort of overwhelming proportions. It is the more remarkable since Einstein is primarily a physicist and only incidentally a mathematician. He came to mathematics rather of necessity than by predilection, and yet he has here developed mathematical formulae and calculations springing from a colossal knowledge.
In 'Marvels at Einstein For His Mathematics', New York Times (4 Feb 1929), 3.
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When a physician is called to a patient, he should decide on the diagnosis, then the prognosis, and then the treatment. … Physicians must know the evolution of the disease, its duration and gravity in order to predict its course and outcome. Here statistics intervene to guide physicians, by teaching them the proportion of mortal cases, and if observation has also shown that the successful and unsuccessful cases can be recognized by certain signs, then the prognosis is more certain.
From An Introduction to the Study of Experimental Medicine (1865), as translated by Henry Copley Greene (1957), 213.
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When an element A has an affinity for another substance B, I see no mechanical reason why it should not take as many atoms of B as are presented to it, and can possibly come into contact with it (which may probably be 12 in general), except so far as the repulsion of the atoms of B among themselves are more than a match for the attraction of an atom of A. Now this repulsion begins with 2 atoms of B to 1 atom of A, in which case the 2 atoms of B are diametrically opposed; it increases with 3 atoms of B to 1 of A, in which case the atoms are only 120° asunder; with 4 atoms of B it is still greater as the distance is then only 90; and so on in proportion to the number of atoms. It is evident from these positions, that, as far as powers of attraction and repulsion are concerned (and we know of no other in chemistry), binary compounds must first be formed in the ordinary course of things, then ternary and so on, till the repulsion of the atoms of B (or A, whichever happens to be on the surface of the other), refuse to admit any more.
Observations on Dr. Bostock's Review of the Atomic Principles of Chemistry', Nicholson's Journal, 1811, 29, 147.
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When chemists have brought their knowledge out of their special laboratories into the laboratory of the world, where chemical combinations are and have been through all time going on in such vast proportions,—when physicists study the laws of moisture, of clouds and storms, in past periods as well as in the present,—when, in short, geologists and zoologists are chemists and physicists, and vice versa,—then we shall learn more of the changes the world has undergone than is possible now that they are separately studied.
Geological Sketches (1866), 73.
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When the formulae of inorganic chemical compounds are considered, even a superficial observer is struck with the general symmetry of their construction; the compounds of nitrogen, phosphorus, antimony and arsenic especially exhibit the tendency of the elements to form compounds containing 3 or 5 equivs. of other elements, and it is in these proportions that their affinities are best satisfied; thus in the ternal group we have NO3, NH3, NI3, NS3, PO3, PH3, PCl3, SbO3, SbH3, SbCl3, AsO3, AsH3, AsCl3 &c; and in the five-atom group NO4, NH4O, NH4I, PO5, PH4I, &c. Without offering any hypothesis regarding the cause of this symmetrical grouping of atoms, it is sufficiently evident, from the examples just given, that such a tendency or law prevails, and that, no matter what the character of the uniting atoms may be, the combining power of the attracting element, if I may be allowed the term, is always satisfied by the same number of these atoms.
'On a New Series of Organic Bodies Containing Metals', Philosophical Transactions of the Royal Society of London, 1852, 14:2, 440.
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Wherever we seek to find constancy we discover change. Having looked at the old woodlands in Hutcheson Forest, at Isle Royale, and in the wilderness of the boundary waters, in the land of the moose and the wolf, and having uncovered the histories hidden within the trees and within the muds, we find that nature undisturbed is not constant in form, structure, or proportion, but changes at every scale of time and space. The old idea of a static landscape, like a single musical chord sounded forever, must be abandoned, for such a landscape never existed except in our imagination. Nature undisturbed by human influence seems more like a symphony whose harmonies arise from variation and change over many scales of time and space, changing with individual births and deaths, local disruptions and recoveries, larger scale responses to climate from one glacial age to another, and to the slower alterations of soils, and yet larger variations between glacial ages.
Discordant Harmonies (1990), 62.
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[Henry Cavendish] fixed the weight of the earth; he established the proportions of the constituents of the air; he occupied himself with the quantitative study of the laws of heat; and lastly, he demonstrated the nature of water and determined its volumetric composition. Earth, air, fire, and water—each and all came within the range of his observations.
Essays in Historical Chemistry (1894), 86.
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[To give insight to statistical information] it occurred to me, that making an appeal to the eye when proportion and magnitude are concerned, is the best and readiest method of conveying a distinct idea.
In The Statistical Breviary: Shewing, on a Principle Entirely New, the Resources of Every State and Kingdom in Europe (1801), 2.
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“I think you’re begging the question,” said Haydock, “and I can see looming ahead one of those terrible exercises in probability where six men have white hats and six men have black hats and you have to work it out by mathematics how likely it is that the hats will get mixed up and in what proportion. If you start thinking about things like that, you would go round the bend. Let me assure you of that!”
In The Mirror Crack’d (1962), 190.
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Carl Sagan Thumbnail In science it often happens that scientists say, 'You know that's a really good argument; my position is mistaken,' and then they would actually change their minds and you never hear that old view from them again. They really do it. It doesn't happen as often as it should, because scientists are human and change is sometimes painful. But it happens every day. I cannot recall the last time something like that happened in politics or religion. (1987) -- Carl Sagan
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- 90 -
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- 80 -
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- 70 -
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- 60 -
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- 50 -
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- 40 -
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- 30 -
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- 20 -
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